bezier_curves.h

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/*
 * This program source code file is part of KiCad, a free EDA CAD application.
 *
 * Copyright The KiCad Developers, see AUTHORS.txt for contributors.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
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 */
 
#ifndef BEZIER_CURVES_H
#define BEZIER_CURVES_H
 
#include <vector>
#include <math/vector2d.h>
 
template <typename T> class ELLIPSE;

class BEZIER_POLY
{
public:
    BEZIER_POLY( const VECTOR2I& aStart, const VECTOR2I& aCtrl1,
                 const VECTOR2I& aCtrl2, const VECTOR2I& aEnd );
 
    BEZIER_POLY( const std::vector<VECTOR2I>& aControlPoints );
 
    BEZIER_POLY( const std::vector<VECTOR2D>& aControlPoints )
        : m_ctrlPts( aControlPoints )
    {
        m_minSegLen = 0.0;
    }

    void GetPoly( std::vector<VECTOR2I>& aOutput, int aMaxError = 10 );
    void GetPoly( std::vector<VECTOR2D>& aOutput, double aMaxError = 10.0 );
 
private:
 
    void getQuadPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
    void getCubicPoly( std::vector<VECTOR2D>& aOutput, double aMaxError );
 
    int findInflectionPoints( double& aT1, double& aT2 );
    int numberOfInflectionPoints();
 
    double thirdControlPointDeviation();
 
    void subdivide( double aT, BEZIER_POLY& aLeft, BEZIER_POLY& aRight );
    void recursiveSegmentation( std::vector<VECTOR2D>& aOutput, double aMaxError );
 
    void cubicParabolicApprox( std::vector<VECTOR2D>& aOutput, double aMaxError );
 
    bool isNaN() const;
 
    bool isFlat( double aMaxError ) const;
 
    VECTOR2D eval( double t );
 
    double m_minSegLen;

    std::vector<VECTOR2D> m_ctrlPts;
};
 
 
// TODO: Refactor BEZIER_POLY to use BEZIER

template <typename NumericType>
class BEZIER
{
public:
    BEZIER() = default;
 
    constexpr BEZIER( const VECTOR2<NumericType>& aStart, const VECTOR2<NumericType>& aC1,
                      const VECTOR2<NumericType>& aC2, const VECTOR2<NumericType>& aEnd ) :
            Start( aStart ), C1( aC1 ), C2( aC2 ), End( aEnd )
    {
    }

    constexpr VECTOR2<NumericType> PointAt( double aT ) const
    {
        const double t2 = aT * aT;
        const double t3 = t2 * aT;
        const double t_m1 = 1.0 - aT;
        const double t_m1_2 = t_m1 * t_m1;
        const double t_m1_3 = t_m1_2 * t_m1;
 
        return ( t_m1_3 * Start ) + ( 3.0 * aT * t_m1_2 * C1 ) + ( 3.0 * t2 * t_m1 * C2 )
               + ( t3 * End );
    }

    constexpr void Split( double aT, BEZIER& aLeft, BEZIER& aRight ) const
    {
        const VECTOR2<NumericType> startC1 = Start + aT * ( C1 - Start );
        const VECTOR2<NumericType> c1C2 = C1 + aT * ( C2 - C1 );
        const VECTOR2<NumericType> c2End = C2 + aT * ( End - C2 );
        const VECTOR2<NumericType> leftC2 = startC1 + aT * ( c1C2 - startC1 );
        const VECTOR2<NumericType> rightC1 = c1C2 + aT * ( c2End - c1C2 );
        const VECTOR2<NumericType> shared = leftC2 + aT * ( rightC1 - leftC2 );
 
        aLeft = BEZIER( Start, startC1, leftC2, shared );
        aRight = BEZIER( shared, rightC1, c2End, End );
    }

    constexpr BEZIER SubCurve( double aT0, double aT1 ) const
    {
        double t0 = aT0;
        double t1 = aT1;
 
        if( t0 < 0.0 )
            t0 = 0.0;
        else if( t0 > 1.0 )
            t0 = 1.0;
 
        if( t1 < 0.0 )
            t1 = 0.0;
        else if( t1 > 1.0 )
            t1 = 1.0;
 
        if( t1 <= t0 )
        {
            const VECTOR2<NumericType> point = PointAt( t0 );
            return BEZIER( point, point, point, point );
        }
 
        if( t0 == 0.0 && t1 == 1.0 )
            return *this;
 
        BEZIER left;
        BEZIER right;
 
        if( t0 == 0.0 )
        {
            Split( t1, left, right );
            return left;
        }
 
        if( t1 == 1.0 )
        {
            Split( t0, left, right );
            return right;
        }
 
        Split( t1, left, right );
 
        BEZIER unused;
        BEZIER subCurve;
        left.Split( t0 / t1, unused, subCurve );
 
        return subCurve;
    }
 
    VECTOR2<NumericType> Start;
    VECTOR2<NumericType> C1;
    VECTOR2<NumericType> C2;
    VECTOR2<NumericType> End;
};

template<typename T>
void TransformEllipseToBeziers( const ELLIPSE<T>& aEllipse, std::vector<BEZIER<T>>& aBeziers );
 
#endif  // BEZIER_CURVES_H